Publication Cover
Applicable Analysis
An International Journal
Volume 97, 2018 - Issue 12
229
Views
13
CrossRef citations to date
0
Altmetric
Articles

A gradient projection method for the sparse signal reconstruction in compressive sensing

&
Pages 2122-2131 | Received 07 Aug 2016, Accepted 07 Jul 2017, Published online: 02 Aug 2017

References

  • Bruckstein A, Donoho D, Elad M. From sparse solutions of systems of equations to sparse modeling of signals and images. SIAM Rev. 2009;51:34–81.
  • Wang H, Zhang H. Hybrid modulation scheme combined with TH-PPM compressive sensing and OFDM. J Comput Infor Sys. 2010;8:2563–2570.
  • Shen SS, Donoho DL, Saunders MA. Atomic decomposition by basis persuit. SIAM Rev. 2001;43:129–159.
  • Donoho DL. For most large underdetemined systems of linear equations, the minimal l1-norm solution is also the sparsest solution. Comm Pure Appl Math. 2006;59:907–934.
  • Donoho DL. Compressed sensing. IEEE Trans Inform Theory. 2006;52:1289–1306.
  • Candès E, Romberg J, Tao T. Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information. IEEE Trans Inform Theory. 2006;52:489–509.
  • Figueiredo MAT, Nowak R, Wright SJ. Gradient projection for sparse reconstruction, application to compressed sensing and other inverse problems. In: IEEE Journal of Selected Topics in Signal Processing. Piscataway (NJ): IEEE Press; 2007. p. 586–597.
  • Xiao YH, Wang QY, Hu QJ. Non-smooth equations based method for l1-norm problems with applications to compressed sensing. Nonlinear Anal: Theory, Methods Appl. 2011;74:3570–3577.
  • Brown PN, Saad Y. Convergence theroy of nonlinear Newton-Krylov algorithms. SIAM J Optim. 1994;4:297–330.
  • Li D, Fukushima M. A global and superlinear convergenct Gauss-Newton-based BFGS method for symmetric nonlinear equations. SIAM J Numer Anal. 1999;37:152–172.
  • Zhou G, Toh KC. Superline convergence of a Newton-type algorithm for monotone equations. J Optim Theory Appl. 2005;125:205–221.
  • Zhou WJ, Li DH. A globally convergent BFGS method for nonlinear monotone equations without any merit functions. Math Comput. 2008;77:2231–2240.
  • Zhou WJ, Li DH. Limited memory BFGS method for nonlinear monotone equations. J Commput Math. 2007;25:89–96.
  • Solodov MV, Svaiter BF. A globally convergent inexact Newton method for systems of monotone equations. In: Fukushima M, Qi L, editor. Reformulation: nonsmooth, piecewise smooth, semismooth and smoothing methods. Dordrecht: Kluwer Academic; 1998. p. 355–369
  • Li QN, Li DH. A class of derivative-free methods for large-scale nonlinear monotone equatiopns. IMA J Numer Anal. 2011;31:1625–1635.
  • Ahookhosh M, Amini K, Bahrami S. Two derivative-free projection approaches for systems of large-scale nonlinear monotone equations. Numer Algor. 2013;64:21–42.
  • Polak E, Ribire G. Note sur la xonvergence de directions conjugees. Rev Francaise informat Recherche Operatinelle 3e Annee. 1969;16:35–43.
  • Hager WW, Zhang H. A survey of nonlinear conjugate gradient methods. Pacific J Optim. 2006;2:35–58.
  • Xiao YH, Zhu H. A conjugate gradient method to solve convex constrained monotone equations with applications in compressive sensing. J Math Anal Appl. 2013;405:310–319.
  • Li DH, Fukushima M. A modified BFGS method and its global convergence in nonconvex minimization. J Comput Appl Math. 2001;129:15–35.
  • Dai YH, Liao LZ. New conjugacy conditions and related nonlinear conjugate gradient methods. Appl Math Optim. 2001;43:87–101.
  • Pang JS. Inexact Newton methods for the nonlinear complementary problem. Math Program. 1986;36:54–71.
  • Wang CW, Wang YJ, Xu CL. A projection method for a system of nonlinear monotone equations with convex constraints. Math Meth Oper Res. 2007;66:33–46.
  • Kim S, Koh K, Lustig M, et al. A method for large-scale 1-regularized least squares problems with applications in signal processing and statistics. Stanford: Dept. of Electrical Engineering, Stanford University; 2007 (Tech Report).

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.